Upconversion photoluminescence is a nonlinear effect where multiple lower energy excitation photons produce higher energy emission photons. This fundamentally interesting process has many applications in biomedical imaging, light source and display technology, and solar energy harvesting. In this review we discuss the underlying physical principles and their modelling using rate equations. We discuss how the understanding of photophysical processes enabled a strategic influence over the optical properties of upconversion especially in rationally designed materials. We subsequently present an overview of recent experimental strategies to control and optimize the optical properties of upconversion nanoparticles, focussing on their emission spectral properties and brightness.